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Time Series of Count Data : Modelling and Estimation

  • Jung, Robert
  • Kukuk, Martin
  • Liesenfeld, Roman

This paper compares various models for time series of counts which can account for discreetness, overdispersion and serial correlation. Besides observation- and parameter-driven models based upon corresponding conditional Poisson distributions, we also consider a dynamic ordered probit model as a flexible specification to capture the salient features of time series of counts. For all models, we present appropriate efficient estimation procedures. For parameter-driven specifications this requires Monte Carlo procedures like simulated Maximum likelihood or Markov Chain Monte-Carlo. The methods including corresponding diagnostic tests are illustrated with data on daily admissions for asthma to a single hospital.

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Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2005,08.

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Date of creation: 2005
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Handle: RePEc:zbw:cauewp:3194
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  1. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
  2. Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
  3. Bauwens, L. & Lubrano, M., 1996. "Bayesian Inference on GARCH Models Using the Gibbs Sampler," G.R.E.Q.A.M. 96a21, Universite Aix-Marseille III.
  4. Jerry A. Hausman & Andrew W. Lo & A. Craig MacKinlay, 1991. "An Ordered Probit Analysis of Transaction Stock Prices," NBER Working Papers 3888, National Bureau of Economic Research, Inc.
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," CORE Discussion Papers 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Tina Hviid Rydberg & Neil Shephard, 2003. "Dynamics of Trade-by-Trade Price Movements: Decomposition and Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 2-25.
  8. Roman Liesenfeld & Ingmar Nolte & Winfried Pohlmeier, 2006. "Modelling financial transaction price movements: a dynamic integer count data model," Empirical Economics, Springer, vol. 30(4), pages 795-825, January.
  9. Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
  10. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
  11. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
  12. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  13. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-35, October.
  14. Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
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